1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let $$f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\}$$. If $${f^{n + 1}}(x) = f({f^n}(x))$$ for all n $$\in$$ N, then $${f^6}(6) + {f^7}(7)$$ is equal to :

A
$${7 \over 6}$$
B
$$- {3 \over 2}$$
C
$${7 \over {12}}$$
D
$$- {{11} \over {12}}$$
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let $$f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$$, $$x \in [ - 1,1]$$. If [a, b] is the range of the function f, then 4a $$-$$ b is equal to :

A
11
B
11 $$-$$ $$\pi$$
C
11 + $$\pi$$
D
15 $$-$$ $$\pi$$
3
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Let f : N $$\to$$ R be a function such that $$f(x + y) = 2f(x)f(y)$$ for natural numbers x and y. If f(1) = 2, then the value of $$\alpha$$ for which

$$\sum\limits_{k = 1}^{10} {f(\alpha + k) = {{512} \over 3}({2^{20}} - 1)}$$

holds, is :

A
2
B
3
C
4
D
6
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Let f : R $$\to$$ R be defined as $$f(x) = {x^3} + x - 5$$. If g(x) is a function such that $$f(g(x)) = x,\forall 'x' \in R$$, then g'(63) is equal to ________________.

A
$${1 \over {49}}$$
B
$${3 \over {49}}$$
C
$${43 \over {49}}$$
D
$${91 \over {49}}$$
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